## Complex Analysis for Mathematics and EngineeringThe New Fifth Edition Of Complex Analysis For Mathematics And Engineering Presents A Comprehensive, Student-Friendly Introduction To Complex Analysis Concepts. Its Clear, Concise Writing Style And Numerous Applications Make The Foundations Of The Subject Matter Easily Accessible To Students. Believing That Mathematicians, Engineers, And Scientists Should Be Exposed To A Careful Presentation Of Mathematics, The Authors Devote Attention To Important Topics, Such As Ensuring That Required Assumptions Are Met Before Using A Theorem, Confirming That Algebraic Operations Are Valid, And Checking That Formulas Are Not Blindly Applied. A New Chapter On Z-Transforms And Applications Provides Students With A Current Look At Digital Filter Design And Signal Processing. |

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### Contents

Complex Numbers | 1 |

Complex Functions | 49 |

Analytic and Harmonic Functions | 93 |

Sequences Julia and Mandelbrot Sets and Power Series | 123 |

Elementary Functions | 155 |

Complex Integration | 193 |

Taylor and Laurent Series | 249 |

Residue Theory | 291 |

### Common terms and phrases

analytic function angle antiderivative Arcsin Arctan bilinear transformation boundary values Calculate Cauchy-Goursat theorem Cauchy-Riemann equations Cauchy's integral formula coefficients complex function complex numbers complex potential compute conformal mapping constant converges uniformly Corollary cosh curve defined definition denote derivative difference equation differentiable Dirichlet problem Evaluate EXAMPLE EXERCISES FOR SECTION expression filter Find the image fluid flow Fourier series given gives harmonic function Hence Identity illustrated in Figure implies inequality inverse Laplace transform Laurent series Let f limit line segment linear obtain one-to-one parametrization point ZQ polynomial positively oriented proof properties quadrant re'e real number residues result Riemann right half-plane root function sequence series representation Show shown in Figure simply connected domain singularity sinh Solution Solve y[n square root streamlines Theorem unit circle upper half-plane vector vertical x-axis z-transform